Problem 1: Mickey Lawson is considering investing some money that he inherited. The following payoff table gives the profits that would be realized during the next year for each of the three investment alternatives Mickey is considering:
a. What decision would maximize expected profile?
b. What is the maximum amount that should be paid for a perfect forecast of the economy?
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State of Nature
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Decision Alternative
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Good Economy
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Bad Economy
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Stock market
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80,000
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(20,000)
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Bonds
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30,000
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20,000
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CD's
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23,000
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23,000
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Probability
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0.5
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0.5
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Problem 2: Today’s electronics specializes in manufacturing modern electronic components. It also builds the equipment that produces the components. Phyllis Weinberger, who is responsible for advising the president of Today’s Electronics on electronic manufacturing equipment, has developed the following table concerning a proposed facility:
a. develop an opportunity loss table
b. what is the mimimax regret decision?
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Profit ($)
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Strong Market
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Fair Market
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Poor Market
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Large facility
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550,000
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110,000
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(310,000)
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Medium sized facility
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30,000
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129,000
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(10,000)
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Samll facility
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20,000
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10,000
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(32,000)
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No facility
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0
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0
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0
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Problem 3: Bill Holiday is not sure what he should do. He can either build a quadplex, build a duplex, gather additional information, or simply do nothing. If he gathers additional information, the results could be either favorable or unfavorable, but it would cost him $3,000 to gather the information. Bill believes that there is a 50-50 chance that the information will be favorable. If the rental market is favorable, Bill will $15,000 with the quadplex or $5,000 with the duplex. Bill doesn’t have the financial resources to do both. With an unfavorable rental market, however, Bill could lose $20,000 with the quadplex or $10,000 with the duplex. Without gathering additional information, Bill estimates that the probability of a favorable rental market is .7. A favorable report from the study would increase the probability of a favorable rental market to .9. Furthermore, an unfavorable report from the additional information would decrease the probability of a favorable rental market to .4. Of course, Bill could forget all of these numbers and do nothing. What is your advice to Bill?
Problem 4: In the past few years, the traffic problems in Lynn McKell’s hometown have gotten worse. Now, Broad Street is congested about half the time. The normal travel time to work for Lynn is only 15 minutes when Broad Street is used and there is no congestion. With congestion, however, it takes Lynn 40 minutes to get to work. If Lynn decides to take the expressway, it will take 30 minutes regardless of the traffic conditions. Lynn’s utility for travel time is:
U(15 minutes) = .9
U(30 minutes) = .7
U(40 minutes) = .2
a. Which route will minimize Lynn’s expected travel time?
b. Which route will maximize Lynn’s utility?
c. When it comes to travel time, is Lynn a risk seeker or risk avoider?